The goal of the proposed research is to investigate the development of numerical thinking in infancy. Number, like time, and space, appears to be one of the fundamental building blocks of adult cognition. Recent data suggests that infants too are sensitive to numerical properties of their environments (see Wynn, 1998 for a review). It is possible that the numerical abilities of infants are homologous to the analog numerical representations hypothesized for adult humans and non-human animals (see Dehaene, et al., 1998). To determine whether the numerical abilities of infants really are the precursors of adult numerical abilities it is important to understand the properties of numerical representations in infancy. Currently, little is known about the format of numerical representations in infancy or of the types of mathematical operations that can be performed on these representations. This proposal seeks evidence for two types of mathematical operations in infants: numerical ordering and ratio comparisons of numerosities. Two sets of experiments are proposed. In the first set of experiments, knowledge of numerical order will be tested in infants. A new paradigm is developed where a sequence of numerosities will be presented in descending or ascending order until the infant habituates to the sequences. Infants will then be tested with sequences of new numerosities in ascending and descending order. If infants represent ordinal relationships between numerosities then they should look longer at the numerical sequences presented in the new ordinal direction. Results will be compared to those obtained from an analogous experiment with stimuli that vary in size rather than number. In a second set of experiments, infants will be habituated to pairs of numerosities that differ by a specific numerical ratio (e.g., 1:2). They will then be tested with new numerosities that differ by the same ratio or a new ratio. If infants appreciate ratio relations between numbers then they should look longer at pairs that have a new ratio. The results of these experiments will provide a better understanding of the similarities and differences between the way infants, adults, and non-human animals process the numerical aspects of their environments. Moreover, understanding how infants process number without language may have important implications for teaching children linguistically-mediated arithmetic computations.